The following will speed up your calculation significantly: 
# Doing $x ** $y can result in very large numbers,
# But if what you want it ( $x ** $y ) % $m, then
# you can pull the modulo into the products and keep
# your numbers smaller.
sub ModuloPwr
{
    my($base,$pwr,$mod) = @_;
    return 1 if $pwr < 1;
    # I probably don't need the 0.1, but doesn't hurt.
    my $result =  ModuloPwr($base, int(0.1 + $pwr/2), $mod);
    $result = ($result * $result) % $mod;
    if ($pwr%2) {
        $result = ( $result * $base ) % $mod;
    }
    return $result;
}

[download]
However there appears to be a bug somewhere. It works fine for small primes, but for instance 97397 is reported not a prime, while it is. (I checked and double-checked. My change does not cause the issue.)

UPDATE
I am a moron. The bug is simple and obvious. Square then reduce modulo the prime works fine until the prime is large enough to go outside of native integer arithmetic. At that point things go haywire.

In reply to Re (tilly) 1: Rabin Miller by tilly
in thread Rabin Miller by Adam

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.